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Mathematics
16 March, 10:51
What are the factors of the equation 24x^2=9-30x?
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Nathaly Terrell
16 March, 11:11
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3 (4x - 1) (2x + 3)
Step-by-step explanation:
Rearrange the equation into standard form
Subtract 9 - 30x from both sides
24x² + 30x - 9 = 0 ← in standard form
Take out 3 as a common factor
3 (8x² + 10x - 3) = 0 ← factor the quadratic
Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x term
product = 8 * - 3 = - 24, sum = 10
The factors are - 2 and + 12
Use these factors to replace the x - term, that is
8x² - 2x + 12x - 3 (factor the first/second and third/fourth terms)
2x (4x - 1) + 3 (4x - 1) ← take out the common factor (4x - 1)
(4x - 1) (2x + 3)
24x² + 30x - 9 = 3 (4x - 1) (2x + 3) ← in factored form
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